Thanks for the clarification, I should have checked before posting. Still, it's slightly over 10 percent of the world's sovereign nations, so most countries manage well enough without a separate government district.

That said, the land occupied by the UN headquarters building and the building spaces is administered by the UN, not a part of US territory, even though the UN has agreed to follow US legislation in exchange for access to utilities and emergency services.

This list is itself misleading. Many more capitals are either their own state or independent cities: Paris is its own département, Berlin its own Land, Madrid is an autonomous city. Others are part of small counties and districts that incorporate several suburbs with the capital in order to integrate the working area of the capital.